That's not quite right Jeff. Einstein wasn't quite consistent with his usage
of the term "mass." As you know I spent a great deal of time and effort
studying the historical background on the concept of mass in physics,
especially as it pertains to special and general relativity. I summarized
the results of that research in an article which is now online at
http://arxiv.org/abs/0709.0687 (first draft)..
Einstein's views on the concept of mass changed over the years. In
Einstein's landmark paper on special relativity Einstein derived an
expression for the "force defined mass" which is defined as m = F/a. The
force defined mass has two values corresponding to directions parallel and
perpendicular to the particles velocity. You probably know these two values
under the names "longitudinal mass" and "transverse mass." Einstein wrote
another paper on the subject of mass in 1906 called "The Principle of
Conservation of the Center of Gravity and the Inertia of Energy," Annalen
der Physik, 20 (1906): 626-633. This is the famous "photon in a box"
gedanken experiment. In this article Einstein stated "If we assign the
electromagnetic field too a mass density (rho_e)...". This means that
Einstein defined a mass density to light. This implies that Einstein thought
of electromagnetic radiation, including light, as having mass.
Forty two years after that paper was published Einstein, in a letter to
Lincoln Barnett dated June 19, 1948, wrote
---------------------------------------------
It is not good to introduce the mass M = m/sqrt( 1 - v^2 /c^2) of a body for
which no clear definition can be given. It is better to introduce no other
mass concept other than the "rest-mass" m. Instead of introducing M it is
better to mention the expression for the momentum and energy of a body in
motion.
---------------------------------------------
As you probably already know, I disagree with Einstein on this point.
Nevertheless, he did say it. Unfortunately this comment has been
misinterpreted. This quote of Einstein's had the unfortunate effect of
leading people to the erroneous conclusion that Einstein never used the
concept of relativistic mass. That is wrong. He *did* use it. He used it in
his text "The Meaning of Relativity." To understand all this one has to bear
in mind the actual definition of relativistic mass. Contrary to what almost
everyone believes, the correct definition of the "relativistic mass of a
particle" is *not* m = gamma*m_0. Relativistic mass is *defined* as the
ratio of the magnitude of the particles 3-momentum to the magnitude of the
particle's 3-velocity (aka "speed"), i.e. m = p/v where m = relativistic
mass, p = magnitude of 3-momentum and v = speed of particle and c is the
magnitude of the speed of light as measured in a vacuum in an inertial frame
of reference.
Here's where the tricky part comes in. When a particle is moving through a
gravitational field with v << c then there is no velocity dependence of m.
However there is still an effect due to the presence of the gravitational
field. You can think of it as the relativistic mass of the particle includes
the mass equivalence of the potential energy of the particle. The zero of
potential being chosen such that clocks located at the a region of space in
which the clocks run at the same rate as the coordinate clocks. For the
Earth the zero of potential is at large distances from the earth (i.e. at
infinity). Therefore there is no velocity dependence but the mass is not
equal to the proper mass. It equals the relativistic mass. Textbooks such as
those by Moller and Mould cover this.
Pete
ps - I just found two articles on relativistic mass online which covers a
brief history of mass in both special and general relativity. I've only
skimmed through them though. The articles seem to be largely based
on/consistent with Lev Okun's articles on the topic of mass. As such there
are areas which leave much to be desired, especially in a couple of articles
by Einstein where he used the concept of relativistic mass. There is web
page for special relativity and one for general relativity. They are located
at
http://www.answers.com/topic/mass-in-special-relativity
http://www.answers.com/topic/mass-in-general-relativity
respectively.
